statistical quality control_final
TRANSCRIPT
-
7/31/2019 Statistical Quality Control_final
1/102
Click to edit Master subtitle style
5/21/12
Statistical Quality
ControlBITS-Pilani, Hyderabad Campus
-
7/31/2019 Statistical Quality Control_final
2/102
5/21/12
Introduction
Have you bought a product andfound it to be defective ?
New backpack with broken zipper
Tablets that are crushed in thestrip/blisters before use
Difficulty in assembling products
requiring minor assembly
As consumers, you expect every
product you buy should perform to
-
7/31/2019 Statistical Quality Control_final
3/102
5/21/12
WHAT IS STATISTICALQUALITY CONTROL?
Statistical quality control (SQC)is the term used to describe the setof statistical tools used by quality
professionals.
It is classified as: Descriptive statistics
Statistical process control
Acceptance sampling
-
7/31/2019 Statistical Quality Control_final
4/102
5/21/12
Classification of SQC
Descriptive statistics
Are used to describe quality characteristicsand relationships.
Included are statistics such as the mean,
standard deviation, the range and ameasure of the distribution of data.
-
7/31/2019 Statistical Quality Control_final
5/102
5/21/12
Classification of SQC cont.
Statistical process control (SPC) A statistical tool that involves inspecting a
random sample of the output from a processand deciding whether the process is
producing products with characteristics thatfall within a pre-determined range.
Acceptance sampling The process of randomly inspecting a
sample of goods and deciding whether toaccept the entire lot based on the results.
-
7/31/2019 Statistical Quality Control_final
6/102
5/21/12
Descriptive statistics are used todescribe certain qualitycharacteristics, such as the centraltendency and variability of observed
data.
Although this is useful, it does notprovide information on whether thereis problem with quality
-
7/31/2019 Statistical Quality Control_final
7/102
5/21/12
Acceptance sampling helps us decidewhether desirable quality has beenachieved for a batch of products, andwhether to accept or reject the items
produced
Although this information is helpful inmaking the quality acceptancedecision after the product has beenproduced, it does not help us identify
and catch a quality problem during
-
7/31/2019 Statistical Quality Control_final
8/102
5/21/12
Statistical QC Tools - Trinity
All three of these statistical qualitycontrol categories are helpful inmeasuring and evaluating the quality
of products or services.
However, statistical process control(SPC) tools are used most frequentlybecause they identify qualityproblems during the production
process.
-
7/31/2019 Statistical Quality Control_final
9/102
5/21/12
:COMMON AND
ASSIGNABLE CAUSES Common, or random causes ofvariation
E.g.: Cola bottles in grocery stores careful observation shows that no twobottles are filled exactly to the samelevel
Common causes of variation arebased on random causes that we
cannot identify
-
7/31/2019 Statistical Quality Control_final
10/102
5/21/12
:COMMON AND
ASSIGNABLE CAUSES It is important to find a range forsuch natural random variation
E.g.: If the average bottle of a soft drinkcontains 16 ounces of liquid, we maydetermine that the amount of naturalvariation is between 15.8 and 16.2ounces.
If production goes out of this range
this would lead us to believe that
-
7/31/2019 Statistical Quality Control_final
11/102
5/21/12
:COMMON AND
ASSIGNABLE CAUSES Assignable causes of variation These are causes that can be identified and
eliminated.
E.g.: poor quality in raw materials, anemployee who needs more training, or amachine in need of repair
In each of these examples the problem canbe identified and corrected.
-
7/31/2019 Statistical Quality Control_final
12/102
5/21/12
Descriptive Statistics
The most important descriptivestatistics are :
Measures of central tendency : Mean(average)
Measures of variability : standarddeviation and range
Measures of the distribution of data
-
7/31/2019 Statistical Quality Control_final
13/102
5/21/12
Descriptive Statistics
The Mean (average)
A statistic that measures the centraltendency of a set of data.
To compute the mean we simply sum allthe observations and divide by the totalnumber of observations.
The equation is given by
-
7/31/2019 Statistical Quality Control_final
14/102
5/21/12
Descriptive Statistics
The Range The difference between the largest and
smallest
observations in a set of data.
Standard Deviation
A statistic that measures the amount ofdata dispersion around the mean.
The equation is given by
-
7/31/2019 Statistical Quality Control_final
15/102
5/21/12
Descriptive Statistics
-
7/31/2019 Statistical Quality Control_final
16/102
5/21/12
Descriptive Statistics
Distribution of data
A third descriptive statistic used tomeasure quality characteristics is the
shape of the distribution of the observeddata.
When a distribution is symmetric, there
are thesame number of observations below and
above the mean.
When a disproportionate number of
-
7/31/2019 Statistical Quality Control_final
17/102
5/21/12
Descriptive Statistics
-
7/31/2019 Statistical Quality Control_final
18/102
5/21/12
Statistical ProcessControl (SPC) Methods
Statistical process control methodsextend the use of descriptivestatistics to monitor the quality of
the product and process.
Using statistical process control wewant to determine the amount ofvariation that is common or normal.
-
7/31/2019 Statistical Quality Control_final
19/102
5/21/12
Developing Control Charts
A control chart (also called processchart or quality control chart) is agraph that shows whether a sample
of data falls within the common ornormal range of variation.
A control chart has upper and lowercontrol limits that separate commonfrom assignable causes of variation.
-
7/31/2019 Statistical Quality Control_final
20/102
5/21/12
Developing Control Charts
The common range of variation isdefined by the use of control chartlimits.
We say that a process is out ofcontrol (out of specification OOS) when a plot of data revealsthat one or more samples fall outsidethe control limits.
-
7/31/2019 Statistical Quality Control_final
21/102
5/21/12
Developing Control Charts
-
7/31/2019 Statistical Quality Control_final
22/102
5/21/12
Developing Control Charts
The upper and lower control limits ona control chart are usually set at 3standard deviations from the mean
If we assume that the data exhibit anormal distribution, these controllimits will capture 99.74 percent ofthe normal variation
-
7/31/2019 Statistical Quality Control_final
23/102
5/21/12
Developing Control Charts
Percentage of values captured bydifferentranges of standard deviation
-
7/31/2019 Statistical Quality Control_final
24/102
5/21/12
Developing Control Charts
From the figure, we can infer that,observations that fall outside the setrange represent assignable causes of
variation.
However, there is a small probabilitythat a value that falls outside thelimits is still due to normal variation.
-
7/31/2019 Statistical Quality Control_final
25/102
5/21/12
Developing Control Charts
Another name for this is alpha risk( ), where alpha refers to the sum ofthe probabilities in both tails of the
distribution that falls outside theconfidence limits.
Chance of Type I error for
3(sigma-standarddeviations)
-
7/31/2019 Statistical Quality Control_final
26/102
5/21/12
Developing Control Charts
For limits of 3 standard deviationsfrom the mean,
the probability of a Type I error is .26% (100% 99.74%),
Whereas,
for limits of 2 standard deviations itis 4.56% (100% 95.44%).
Chance of Type I error for
3(sigma-standarddeviations)
-
7/31/2019 Statistical Quality Control_final
27/102
5/21/12
Types of Quality ControlCharts
Control charts are one of the mostcommonly used tools in statisticalprocess control.
The different characteristics that canbe measured by control charts canbe divided into two groups:
1. Variables
1. Attributes
-
7/31/2019 Statistical Quality Control_final
28/102
5/21/12
Types of Quality ControlCharts
Control chart for variables
A control chart for variables is usedto monitor
characteristics that can be measuredand have
a continuum of values, such asheight, weight,
or volume.
-
7/31/2019 Statistical Quality Control_final
29/102
5/21/12
Types of Quality ControlCharts
Control chart for attributes
A control chart for attributes is usedto monitor a product characteristicthat has a discrete value and can becounted.
Often they can be evaluated with asimple
yes or no decision
Examples include color, taste, or smell.
-
7/31/2019 Statistical Quality Control_final
30/102
5/21/12
Control Charts forVariables
When an item is inspected, thevariable being monitored ismeasured and recorded
For example, if we were producingcandles, height might be animportant variable.
Two of the most commonly usedcontrol charts for variables monitorboth the central tendency of the data
(the mean) and the variability of the
-
7/31/2019 Statistical Quality Control_final
31/102
5/21/12
Control Charts forVariables
Mean (x-bar) Charts
A control chart used to monitor changes inthe mean value of a process.
To construct a mean chart we first need toconstruct the centre line of the chart.
To do this we take multiple samples andcompute their means.
Usually these samples are small, with aboutfour or five observations.
Each sample has its own mean,
-
7/31/2019 Statistical Quality Control_final
32/102
5/21/12
Control Charts forVariables
Mean (x-bar) Charts
The centre line of the chart is then computed as the mean of allsample means, where is the number of samples
-
7/31/2019 Statistical Quality Control_final
33/102
5/21/12
Control Charts forVariables
Mean (x-bar) Charts
-
7/31/2019 Statistical Quality Control_final
34/102
5/21/12
-
7/31/2019 Statistical Quality Control_final
35/102
5/21/12
-
7/31/2019 Statistical Quality Control_final
36/102
5/21/12
Mean (x-bar) Charts
Another way to construct the controllimits is to use the sample range asan estimate of the variability of the
process. The range is simply the difference
between the largest and smallest
values in the sample The spread of the range can tell us
about the variability of the data.
-
7/31/2019 Statistical Quality Control_final
37/102
5/21/12
Mean (x-bar) Charts
Factors for three-sigma control
-
7/31/2019 Statistical Quality Control_final
38/102
5/21/12
ac o s o ee s g a co olimits of and R-charts
-
7/31/2019 Statistical Quality Control_final
39/102
5/21/12
Constructing a Mean (x-Bar)Chart from the Sample Range
-
7/31/2019 Statistical Quality Control_final
40/102
5/21/12
Range (R) Charts
A control chart that monitorschanges in the dispersion orvariability of process.
While x-bar charts measure shift inthe central tendency of the process,range charts monitor the dispersionor variability of the process.
-
7/31/2019 Statistical Quality Control_final
41/102
5/21/12
Range (R) Charts
The centre line of the control chart isthe average range, and the upperand lower control limits are
computed as :
-
7/31/2019 Statistical Quality Control_final
42/102
5/21/12
Range (R) Charts Note thatA2 is a factor that includes three standard
deviations of ranges and is dependent on thesample size being considered.
( ) h
-
7/31/2019 Statistical Quality Control_final
43/102
5/21/12
Range (R) Charts Resulting chart is depicted below:
Using Mean and Range Charts
-
7/31/2019 Statistical Quality Control_final
44/102
5/21/12
Using Mean and Range ChartsTogether
The mean or x-bar chart measures the centraltendency of the process, whereas the range chartmeasures the dispersion or variance of the process.
Since both variables are important, it makes senseto monitor a process using both mean and rangecharts.
It is possible to have a shift in the mean of theproduct but not a change in the dispersion.
Using Mean and Range Charts
-
7/31/2019 Statistical Quality Control_final
45/102
5/21/12
Using Mean and Range ChartsTogether
Process shifts captured by chartsand -charts
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
46/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
P-chart
A control chart that monitors theproportion of defects in a sample.
C-chart
A control chart used to monitor thenumberof
defects per unit.
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
47/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
The P-Chart (Proportion chart)
P-charts are used to measure the proportionof items in a sample that are defective.
E.g.: proportion of broken tablets in a batch
P-charts are appropriate when both thenumber of defectives measured and the sizeof the total sample can be counted.
A proportion can then be computed andused as the statistic of measurement.
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
48/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
P-chart is a control chart that monitorstheproportion of defects in a sample.
The center line is computed as theaverage proportion defective in thepopulation.
This is obtained by taking a number ofsamples of observations at random andcomputing the average value of p acrossall sam les.
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
49/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
To construct the upper and lower controllimits for a p-chart, we use the followingformula:
As with the other charts,zis selected to be either 2or 3 standard deviations, depending on the amountof data we wish to capture in our control limits
Usually z = 3
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
50/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
-
7/31/2019 Statistical Quality Control_final
51/102
5/21/12
-
7/31/2019 Statistical Quality Control_final
52/102
5/21/12
In this example the lowercontrol limit is negative,
which sometimes occursbecause the computationis an approximation of thebinomial distribution. Whenthis occurs, the LCL isrounded up tozero because we cannot
have a negative controllimit.
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
53/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
The C-Chart (Count chart)
C-charts count the actual number of defects.
E.g.: Number of cfu on a petri-dish
C-charts do not give the proportion (we
cannot compute proportion of bacteria onpetri dish).
In C-charts, the types of units ofmeasurement we consider are a eriod of
CONTROL CHARTS FOR
-
7/31/2019 Statistical Quality Control_final
54/102
5/21/12
CONTROL CHARTS FORATTRIBUTES
The C-Chart (Count chart)
The average number of defects, is thecenter line of the control chart.
The upper and lower control limits arecomputed as follows:
-
7/31/2019 Statistical Quality Control_final
55/102
5/21/12
-
7/31/2019 Statistical Quality Control_final
56/102
5/21/12
Process Capability
Process capability
The ability of a production process tomeet or exceed preset specifications.
Product specifications(tolerances)
They preset ranges of acceptable qualitycharacteristics, such as productdimensions.
For a product to be considered
-
7/31/2019 Statistical Quality Control_final
57/102
5/21/12
Process Capability
E.g. for product specification:
Thickness of a particular tablet set at3.3 0.2 mm
It means, the standard requiredthickness of the tablet must be 3.3 mm,though, it is acceptable if it falls
between 3.1 to 3.5 mm
Specifications for a product are
preset on the basis of how the
-
7/31/2019 Statistical Quality Control_final
58/102
5/21/12
Process Capability
Measuring Process Capability
Simply setting up control charts to monitorwhether a process is in control does not
guarantee process capability.
Process capability is measured by theprocess capability index, Cp,
Cp is computed as the ratio of thespecification width to the width of the processvariability:
P C bilit
-
7/31/2019 Statistical Quality Control_final
59/102
5/21/12
Process Capability
Measuring Process CapabilityWhere, the specification width is thedifference between the upper specificationlimit (USL) and the lower specification limit
(LSL) of the process
The process width computed as 6 standard
deviations of the process being monitored
The reason we use 6 is that most of theprocess measurement (99.74 percent) falls
within 3 SD, which is a total of 6 standard
-
7/31/2019 Statistical Quality Control_final
60/102
5/21/12
Cp = 1 Cp < 1
Cp > 1
-
7/31/2019 Statistical Quality Control_final
61/102
5/21/12
2
1
3A Cp value of 1 means that 99.74 percent of the productsproduced will fall within the specification limits.
This also means that .26 percent (100% 99.74%) of the
products will not be acceptable.
The number .26 percent corresponds to 2600 parts per million(ppm) defective(0.0026 1,000,000)
That number can seem very high if we think of it in terms of
-
7/31/2019 Statistical Quality Control_final
62/102
5/21/12
-
7/31/2019 Statistical Quality Control_final
63/102
5/21/12
Computation ofCp when processvariability not centered across
specification width
-
7/31/2019 Statistical Quality Control_final
64/102
5/21/12
In the figure the specification limitsare set between 15.8 and 16.2
ounces, with a mean of 16.0 ounces.
However, the process variation is notcentered; it has a mean of 15.9ounces.
Because of this, a certain proportionof products will fall outside thespecification range.
-
7/31/2019 Statistical Quality Control_final
65/102
5/21/12
Computation for such samples aredone as follows:
This measure of process capability helps us address apossible lack of centering of the process over thespecification range
To use this measure, the process capability of each halfof the normal distribution is computed and theminimum of the two is used.
-
7/31/2019 Statistical Quality Control_final
66/102
5/21/12
Example:
The Cp value of 1.00 leads us to conclude that the
process is capable.
However, from the graph we can see that theprocess is notcentered on the specification rangeand is producing out-of-spec products.
-
7/31/2019 Statistical Quality Control_final
67/102
5/21/12
Example:
Using only the Cp measure would lead to an
incorrect conclusion in this case
Computing Cpkgives us a different answer and leads us to adifferent conclusion:
-
7/31/2019 Statistical Quality Control_final
68/102
5/21/12
60
-
7/31/2019 Statistical Quality Control_final
69/102
5/21/12
Six Sigma Principles
The term Six Sigma was coined bythe Motorola Corporation in the1980s to describe the high level ofquality the company was striving toachieve.
Sigma ( ) stands for the number ofstandard deviations of the process
3 sigma ( ) means that 2600 m
Six sigma principles
-
7/31/2019 Statistical Quality Control_final
70/102
5/21/12
Six sigma principles
PPM defective for 3 versus 6 quality (not toscale)
-
7/31/2019 Statistical Quality Control_final
71/102
5/21/12
Acceptance Sampling
Acceptance sampling, refers to theprocess of randomly inspecting acertain number of items from a lot or
batch in order to decide whether toaccept or reject the entire batch.
Acceptance sampling is performedeither before or afterthe process,rather than during the process.
-
7/31/2019 Statistical Quality Control_final
72/102
5/21/12
Acceptance sampling before theprocess involves sampling materialsreceived from a supplier (E.g.: Rawmaterials for tablet manufacture)
Sampling afterthe process involves
sampling finished items that are tobe shipped either to a customer or toa distribution center (E.g.: Packedtablet bottles in warehouse)
-
7/31/2019 Statistical Quality Control_final
73/102
5/21/12
Acceptance sampling is used wheninspecting every item is notphysically possible or would beoverly expensive, or when inspecting
a large number of items would leadto errors due to worker fatigue
Another example of whenacceptance sampling would be usedis in destructive testing (E.g.:
Measurin crushin stren th of
Sampling Plans in
-
7/31/2019 Statistical Quality Control_final
74/102
5/21/12
Sampling Plans inacceptance sampling
Sampling Plan
A plan for acceptance sampling thatprecisely specifies the parameters of thesampling process and theacceptance/rejection criteria.
The variables to be specified include the size
of the lot (N), the size of the sampleinspected from the lot (n), the number ofdefects above which a lot is rejected (c), andthe number of samples that will be taken.
Sampling Plans in
-
7/31/2019 Statistical Quality Control_final
75/102
5/21/12
Sampling Plans inacceptance sampling
Sampling Plan
In single sampling, in which a randomsample is drawn from every lot, each item isclassified as either good or bad
Depending on number of bad items found,the entire batch is rejected
Sampling Plans in
-
7/31/2019 Statistical Quality Control_final
76/102
5/21/12
Sampling Plans inacceptance sampling
Sampling Plan Another type of acceptance sampling is
called double sampling
This provides an opportunity to sample thelot a second time if the results of the firstsample are inconclusive.
In double sampling we first sample a lot of
goods according to preset criteria fordefinite acceptance or rejection.
However, if the results fall in the middlerange, they are considered inconclusive and
a second sample is taken
pera ng arac er s c(OC) C
-
7/31/2019 Statistical Quality Control_final
77/102
5/21/12
p g(OC) Curves
OC Curves
A graph that shows the probability or chanceof accepting a lot given various proportionsof defects in the lot.
QC C
-
7/31/2019 Statistical Quality Control_final
78/102
5/21/12
QC Curves
Acceptable quality level (AQL)
The small percentage of defects thatconsumers are willing to accept.
Lot tolerance percent defective
(LTPD) The upper limit of the percentage of
defective items consumers are willing
to tolerate.
OC
-
7/31/2019 Statistical Quality Control_final
79/102
5/21/12
OC curves
Consumers risk
The chance of accepting a lot thatcontains a greater number of defects
than the LTPD limit.
This is the probability of making aType II errorthat is, accepting a lotthat is truly bad.
An OC curve showing producersi k ( ) d
-
7/31/2019 Statistical Quality Control_final
80/102
5/21/12
risk ( ) andconsumers risk ()
OC
-
7/31/2019 Statistical Quality Control_final
81/102
5/21/12
OC curves
Producers risk
The chance that a lot containing anacceptable
quality level will be rejected.
This is the probability of making aType I errorthat is, rejecting a lotthat is good.
OC curves
-
7/31/2019 Statistical Quality Control_final
82/102
5/21/12
OC curves
We can determine from an OC curvewhat the consumers and producersrisks are.
However, these values should not beleft to chance.
Rather, sampling plans are usuallydesigned to meet specific levels of
consumers and producers risk.
D l i OC C
-
7/31/2019 Statistical Quality Control_final
83/102
5/21/12
Developing OC Curves
An OC curve graphically depicts thediscriminating power of a samplingplan.
To draw an OC curve, we typicallyuse a cumulative binomial
distribution to obtain probabilities ofaccepting a lot given varying levelsof lot defects.
D l i OC C
-
7/31/2019 Statistical Quality Control_final
84/102
5/21/12
Developing OC Curves
Partial Cumulative Binomial Probability Table
The top of the table shows values ofp, whichrepresents the proportionof defective items in a lot (5 percent, 10 percent, 20percent, etc.).
The left-hand column shows values ofn, whichrepresent the sample size being considered
Developing OC Curves
-
7/31/2019 Statistical Quality Control_final
85/102
5/21/12
Developing OC Curves
Developing OC Curves
-
7/31/2019 Statistical Quality Control_final
86/102
5/21/12
Developing OC CurvesOC curve with n = 5and c = 1
Average Outgoing
-
7/31/2019 Statistical Quality Control_final
87/102
5/21/12
g g gQuality (AOQ)
Average outgoing quality (AOQ)
The expected proportion of defectiveitems that will be passed to the
customer under the sampling plan.
From the OC curves, higher thequality of the lot, the higher is thechance that it will be accepted
Average Outgoing
-
7/31/2019 Statistical Quality Control_final
88/102
5/21/12
g g gQuality (AOQ)
Given that some lots are acceptedand some rejected, it is useful tocompute the average outgoing
quality (AOQ) of lots to get a senseof the overall outgoing quality of theproduct.
Assuming that all lots have the sameproportion of defective items, the
average outgoing quality can be
Average Outgoing
-
7/31/2019 Statistical Quality Control_final
89/102
5/21/12
g g gQuality (AOQ)
Usually we assume the fraction in the previous
equation to equal 1 and simplify the equation to thefollowing form:
-
7/31/2019 Statistical Quality Control_final
90/102
How much and how often
-
7/31/2019 Statistical Quality Control_final
91/102
5/21/12
to inspect ? Consider Product Cost and
Product Volume
trade-off between the cost of inspection
and the cost of passing on a defectiveitem should be considered
The inspection process should be set up
to consider issues of product cost andvolume.
Historical data must be considered
How much and how often
-
7/31/2019 Statistical Quality Control_final
92/102
5/21/12
to inspect ? Consider Process Stability
Stable processes that do not changefrequently do not need to be inspected
often. On the other hand, processes that are
unstable and change often should beinspected frequently.
For example, if it has been observedthat a particular type of drilling machinein a machine shop often goes out of
tolerance, that machine should be
How much and how often
-
7/31/2019 Statistical Quality Control_final
93/102
5/21/12
to inspect ? Consider Lot Size
The size of the lot or batch beingproduced is another factor to consider in
determining the amount of inspection A company that produces a small
number of large lots will have a smallernumber of inspections than a companythat produces a large number of smalllots
The reason is that every lot should have
some inspection, and when lots are
Where to Inspect ?
-
7/31/2019 Statistical Quality Control_final
94/102
5/21/12
Where to Inspect ?
Inbound Materials
Finished Products
Prior to Costly Processing
Which tools to use ?
-
7/31/2019 Statistical Quality Control_final
95/102
5/21/12
Which tools to use ?
Tools such as control charts are bestused at various points in theproduction process.
Acceptance sampling is best used forinbound and outbound materials.
It is also the easiest method to use
for attribute measures, whereas
Conclusions
-
7/31/2019 Statistical Quality Control_final
96/102
5/21/12
Conclusions
Statistical quality control can bedivided into three broad categories:descriptive statistics, acceptance
sampling, and statistical processcontrol (SPC).
Descriptive statistics are used todescribe quality characteristics, suchas the mean, range, and variance.
Conclusions
-
7/31/2019 Statistical Quality Control_final
97/102
5/21/12
Conclusions
Statistical process control (SPC)involves inspecting a random sampleof output from a process and
deciding whether the process isproducing products withcharacteristics that fall within presetspecifications.
There are two causes of variation in
the quality of a product or process:
Conclusions
-
7/31/2019 Statistical Quality Control_final
98/102
5/21/12
Conclusions
Common causes of variation arerandom causes that we cannotidentify.
Assignable causes of variation arethose that can be identified andeliminated.
A control chart is a graph used instatistical process control that shows
whether a sam le of data falls within
Conclusions
-
7/31/2019 Statistical Quality Control_final
99/102
5/21/12
Conclusions
Control charts for variables include x-bar charts and R-charts.
X-bar charts monitor the mean oraverage value of a productcharacteristic
R-charts monitor the range or
dispersion of the values of a product
Conclusions
-
7/31/2019 Statistical Quality Control_final
100/102
5/21/12
Conclusions
P-charts are used to monitor theproportion of defects in a sample.
C-charts are used to monitor theactual number of defects in asample.
Process capability is the ability of theproduction process to meet or
exceed reset s ecifications
Conclusions
-
7/31/2019 Statistical Quality Control_final
101/102
5/21/12
Conclusions
The term Six Sigma indicates a levelof quality in which the number ofdefects is no more than 3.4 parts permillion.
The goal of acceptance sampling is
to determine criteria for acceptanceor rejection based on lot size, samplesize, and the desired level ofconfidence.
Conclusions
-
7/31/2019 Statistical Quality Control_final
102/102
Conclusions
Operating characteristic (OC) curvesare graphs that show thediscriminating power of a samplingplan.